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|
MODULE gti_reduce
USE global
USE si_reduce
USE pave_reduce
USE funlib
USE ti_reduce
IMPLICIT NONE
CONTAINS
SUBROUTINE general_ti_reduce(IMODE,NLOOPLINE,idim_init,indices_init,MAXRANK,NCOEFS,PDEN,M2L,MU,TICOEFS,TSTABLE)
! IMODE=0, IBP reduction
! IMODE=1, PaVe reduction
IMPLICIT NONE
INTEGER,INTENT(IN)::NLOOPLINE,MAXRANK,IMODE,NCOEFS,idim_init
INTEGER,DIMENSION(NLOOPLINE),INTENT(IN)::indices_init
REAL(KIND(1d0)),INTENT(IN)::MU
REAL(KIND(1d0)),DIMENSION(NLOOPLINE,0:3),INTENT(IN)::PDEN
REAL(KIND(1d0)),DIMENSION(NLOOPLINE),INTENT(IN)::M2L
COMPLEX(KIND(1d0)),DIMENSION(0:NCOEFS-1,1:4),INTENT(OUT)::TICOEFS
LOGICAL,INTENT(OUT)::TSTABLE
INTEGER,DIMENSION(1,1)::sol11
REAL(KIND(1d0)),DIMENSION(1)::factor1
INTEGER::first=0,i,j,jk,numzerp,n,r,nr,init,ntot
INTEGER,DIMENSION(NLOOPLINE)::zerp
! f[i,n]=(i+n-1)!/(n-1)!/i!
! nmax=5,rmax=6,NLOOPLINE=nmax+1
! see syntensor in ti_reduce.f90
! xiarraymax2=(f[0,nmax])+(f[1,nmax])+(f[2,nmax]+f[0,nmax])
! +(f[3,nmax]+f[1,nmax])+(f[4,nmax]+f[2,nmax]+f[0,nmax])
! +(f[5,nmax]+f[3,nmax]+f[1,nmax])+(f[6,nmax]+f[4,nmax]+f[2,nmax]+f[0,nmax])
! when rmax=5,nmax=5 -> xiarraymax2=314
! when rmax=6,nmax=5 -> xiarraymax2=610
INTEGER::xiarraymax2,xiarraymax,xiarraymax3
!REAL(KIND(1d0)),DIMENSION(xiarraymax2)::syfactor
REAL(KIND(1d0)),DIMENSION(:),ALLOCATABLE::syfactor
!INTEGER,DIMENSION(xiarraymax2,-1:NLOOPLINE)::sy
INTEGER,DIMENSION(:,:),ALLOCATABLE::sy
! REAL(KIND(1d0)),PARAMETER::EPS=1d-10
REAL(KIND(1d0))::temp
INTEGER,DIMENSION(NLOOPLINE)::indices_init2
SAVE first,xiarraymax,xiarraymax2,xiarraymax3,syfactor,sy
MU_R_IREGI=MU
IF(first.EQ.0)THEN
IF(.NOT.print_banner)THEN
INCLUDE "banner.inc"
print_banner=.TRUE.
ENDIF
xiarraymax2=0
DO i=0,MAXRANK_IREGI
j=i/2+1
DO jk=1,j
xiarraymax2=xiarraymax2+&
xiarray_arg1(2*jk-2+MOD(i,2),MAXNLOOP_IREGI-1)
ENDDO
ENDDO
xiarraymax=xiarray_arg1(MAXRANK_IREGI,MAXNLOOP_IREGI-1)
xiarraymax3=xiarray_arg1(MAXRANK_IREGI,4)
IF(.NOT.ALLOCATED(syfactor))THEN
ALLOCATE(syfactor(xiarraymax2))
ENDIF
IF(.NOT.ALLOCATED(sy))THEN
ALLOCATE(sy(xiarraymax2,-1:MAXNLOOP_IREGI))
ENDIF
! initialization xiarray and metric, factorial_pair
CALL all_Integers(1,1,1,sol11,factor1)
CALL calc_factorial_pair
DO i=0,3
DO j=0,3
IF(i.NE.j)THEN
metric(i,j)=0d0
ELSEIF(i.EQ.0)THEN
metric(i,j)=1d0
ELSE
metric(i,j)=-1d0
ENDIF
ENDDO
END DO
first=1
ENDIF
IF(MOD(idim_init,2).NE.0)THEN
WRITE(*,*)"ERROR: the initial idim=d-4+2*eps should be even in general_ti_reduce ",idim_init
STOP
ENDIF
numzerp=0
DO i=1,NLOOPLINE
temp=(ABS(PDEN(i,0))+ABS(PDEN(i,1))+ABS(PDEN(i,2))+ABS(PDEN(i,3)))/4d0
IF(temp.LT.EPS)THEN
zerp(i)=0
numzerp=numzerp+1
ELSE
zerp(i)=1
indices_init2(i-numzerp)=indices_init(i)
ENDIF
ENDDO
n=NLOOPLINE-numzerp
IF(n.GE.MAXNLOOP_IREGI.OR.MAXRANK.GT.MAXRANK_IREGI)THEN
WRITE(*,100)"ERROR: out of range of general_ti_reduce (N<=",MAXNLOOP_IREGI,",R<=",MAXRANK_IREGI,")"
STOP
ENDIF
CALL general_sytensor(n,indices_init2(1:n),MAXRANK,xiarraymax,xiarraymax2,ntot,&
sy(1:xiarraymax2,-1:n),syfactor(1:xiarraymax2))
CALL general_symmetry(IMODE,NLOOPLINE,idim_init,indices_init,ntot,xiarraymax,xiarraymax2,xiarraymax3,&
sy(1:xiarraymax2,-1:n),&
syfactor(1:xiarraymax2),numzerp,zerp,PDEN,M2L,NCOEFS,TICOEFS)
TSTABLE=STABLE_IREGI
RETURN
100 FORMAT(2X,A45,I2,A4,I2,A1)
END SUBROUTINE general_ti_reduce
SUBROUTINE general_ti_reduce2(IMODE,NLOOPLINE,idim_init,indices_init,MAXRANK,NCOEFS,PDEN,PijMatrix,M2L,MU,TICOEFS,TSTABLE)
! IMODE=0, IBP reduction
! IMODE=1, PaVe reduction
IMPLICIT NONE
INTEGER,INTENT(IN)::NLOOPLINE,MAXRANK,IMODE,NCOEFS,idim_init
INTEGER,DIMENSION(NLOOPLINE),INTENT(IN)::indices_init
REAL(KIND(1d0)),INTENT(IN)::MU
REAL(KIND(1d0)),DIMENSION(NLOOPLINE,0:3),INTENT(IN)::PDEN
REAL(KIND(1d0)),DIMENSION(NLOOPLINE,NLOOPLINE),INTENT(IN)::PijMatrix
REAL(KIND(1d0)),DIMENSION(NLOOPLINE),INTENT(IN)::M2L
COMPLEX(KIND(1d0)),DIMENSION(0:NCOEFS-1,1:4),INTENT(OUT)::TICOEFS
LOGICAL,INTENT(OUT)::TSTABLE
INTEGER,DIMENSION(1,1)::sol11
REAL(KIND(1d0)),DIMENSION(1)::factor1
INTEGER::first=0,i,j,jk,numzerp,n,r,nr,init,ntot
INTEGER,DIMENSION(NLOOPLINE)::zerp
! f[i,n]=(i+n-1)!/(n-1)!/i!
! nmax=5,rmax=6,NLOOPLINE=nmax+1
! see syntensor in ti_reduce.f90
! xiarraymax2=(f[0,nmax])+(f[1,nmax])+(f[2,nmax]+f[0,nmax])
! +(f[3,nmax]+f[1,nmax])+(f[4,nmax]+f[2,nmax]+f[0,nmax])
! +(f[5,nmax]+f[3,nmax]+f[1,nmax])+(f[6,nmax]+f[4,nmax]+f[2,nmax]+f[0,nmax])
! when rmax=5,nmax=5 -> xiarraymax2=314
! when rmax=6,nmax=5 -> xiarraymax2=610
INTEGER::xiarraymax2,xiarraymax,xiarraymax3
REAL(KIND(1d0)),DIMENSION(:),ALLOCATABLE::syfactor
!INTEGER,DIMENSION(xiarraymax2,-1:NLOOPLINE)::sy
INTEGER,DIMENSION(:,:),ALLOCATABLE::sy
REAL(KIND(1d0))::temp
INTEGER,DIMENSION(NLOOPLINE)::indices_init2
SAVE first,xiarraymax,xiarraymax2,xiarraymax3,syfactor,sy
MU_R_IREGI=MU
IF(first.EQ.0)THEN
IF(.NOT.print_banner)THEN
INCLUDE "banner.inc"
print_banner=.TRUE.
ENDIF
xiarraymax2=0
DO i=0,MAXRANK_IREGI
j=i/2+1
DO jk=1,j
xiarraymax2=xiarraymax2+&
xiarray_arg1(2*jk-2+MOD(i,2),MAXNLOOP_IREGI-1)
ENDDO
ENDDO
xiarraymax=xiarray_arg1(MAXRANK_IREGI,MAXNLOOP_IREGI-1)
xiarraymax3=xiarray_arg1(MAXRANK_IREGI,4)
IF(.NOT.ALLOCATED(syfactor))THEN
ALLOCATE(syfactor(xiarraymax2))
ENDIF
IF(.NOT.ALLOCATED(sy))THEN
ALLOCATE(sy(xiarraymax2,-1:MAXNLOOP_IREGI))
ENDIF
! initialization xiarray and metric,factorial_pair
CALL all_Integers(1,1,1,sol11,factor1)
CALL calc_factorial_pair
DO i=0,3
DO j=0,3
IF(i.NE.j)THEN
metric(i,j)=0d0
ELSEIF(i.EQ.0)THEN
metric(i,j)=1d0
ELSE
metric(i,j)=-1d0
ENDIF
ENDDO
END DO
first=1
ENDIF
IF(MOD(idim_init,2).NE.0)THEN
WRITE(*,*)"ERROR: the initial idim=d-4+2*eps should be even in general_ti_reduce2 ",idim_init
STOP
ENDIF
numzerp=0
DO i=1,NLOOPLINE
temp=(ABS(PDEN(i,0))+ABS(PDEN(i,1))+ABS(PDEN(i,2))+ABS(PDEN(i,3)))/4d0
IF(temp.LT.EPS)THEN
zerp(i)=0
numzerp=numzerp+1
ELSE
zerp(i)=1
indices_init2(i-numzerp)=indices_init(i)
ENDIF
ENDDO
n=NLOOPLINE-numzerp
IF(n.GE.MAXNLOOP_IREGI.OR.MAXRANK.GT.MAXRANK_IREGI)THEN
WRITE(*,100)"ERROR: out of range of general_ti_reduce2 (N<=",MAXNLOOP_IREGI,",R<=",MAXRANK_IREGI,")"
STOP
ENDIF
CALL general_sytensor(n,indices_init2(1:n),MAXRANK,xiarraymax,xiarraymax2,ntot,&
sy(1:xiarraymax2,-1:n),syfactor(1:xiarraymax2))
CALL general_symmetry2(IMODE,NLOOPLINE,idim_init,indices_init,ntot,xiarraymax,xiarraymax2,xiarraymax3,&
sy(1:xiarraymax2,-1:n),&
syfactor(1:xiarraymax2),numzerp,zerp,PDEN,PijMatrix,M2L,NCOEFS,TICOEFS)
TSTABLE=STABLE_IREGI
RETURN
100 FORMAT(2X,A46,I2,A4,I2,A1)
END SUBROUTINE general_ti_reduce2
SUBROUTINE general_sytensor(n,indices_init2,rmax,xiarraymax,xiarraymax2,ntot,sy,syfactor)
IMPLICIT NONE
INTEGER,INTENT(IN)::n,rmax,xiarraymax2,xiarraymax
INTEGER,DIMENSION(n),INTENT(IN)::indices_init2
INTEGER,INTENT(OUT)::ntot
INTEGER,DIMENSION(xiarraymax2,-1:n),INTENT(OUT)::sy
!INTEGER,DIMENSION(*,*),INTENT(OUT)::sy
INTEGER::r,i,j,k,i0,i0max,rm2x0,nntot,init
INTEGER,DIMENSION(xiarraymax,n)::sol
REAL(KIND(1d0)),DIMENSION(xiarraymax2),INTENT(OUT)::syfactor
REAL(KIND(1d0)),DIMENSION(xiarraymax)::factor
REAL(KIND(1d0)),DIMENSION(xiarraymax)::factor_temp
IF(n.EQ.0)THEN
init=1
DO r=0,rmax
IF(MOD(r,2).NE.0)CYCLE
i0max=r/2
sy(init,-1)=r
sy(init,0)=i0max
syfactor(init)=1d0/pi**(r-i0max)/(-2)**i0max
init=init+1
ENDDO
ntot=init-1
RETURN
ENDIF
! 2*x0+x1+x2+...+xn=r
init=1
DO r=0,rmax
i0max=r/2
DO i=0,i0max
rm2x0=r-2*i
IF(n.LT.2)THEN
nntot=1
ELSE
nntot=ntot_xiarray(rm2x0,n)
ENDIF
CALL all_integers(n,nntot,rm2x0,sol(1:nntot,1:n),factor(1:nntot))
sy(init:init+nntot-1,-1)=r
sy(init:init+nntot-1,0)=i
sy(init:init+nntot-1,1:n)=sol(1:nntot,1:n)
! general form, the following can be optimized
factor_temp(1:nntot)=1d0
DO j=1,n
DO k=1,nntot
factor_temp(k)=factor_temp(k)&
*factorial_pair(indices_init2(j),sol(k,j))
ENDDO
ENDDO
syfactor(init:init+nntot-1)=1d0/factor(1:nntot)*DBLE(factorial(rm2x0))&
/pi**(r-i)/(-2)**i
syfactor(init:init+nntot-1)=syfactor(init:init+nntot-1)*factor_temp(1:nntot)
init=init+nntot
ENDDO
ENDDO
ntot=init-1
RETURN
END SUBROUTINE general_sytensor
SUBROUTINE general_symmetry2(IMODE,NLOOPLINE,idim_init,indices_init,ntot,xiarraymax,xiarraymax2,xiarraymax3,&
sy,syfactor,numzerp,zerp,PDEN,PijMatrix,M2L,NCOEFS,coefs)
! IMODE=0, IBP reduction
! IMODE=1, PaVe reduction
IMPLICIT NONE
INTEGER,INTENT(IN)::ntot,numzerp,NLOOPLINE,IMODE,NCOEFS,idim_init,xiarraymax2,xiarraymax,xiarraymax3
INTEGER,DIMENSION(NLOOPLINE),INTENT(IN)::indices_init
INTEGER,DIMENSION(xiarraymax2,-1:NLOOPLINE-numzerp),INTENT(IN)::sy
!INTEGER,DIMENSION(*,*),INTENT(IN)::sy
REAL(KIND(1d0)),DIMENSION(xiarraymax2),INTENT(IN)::syfactor
INTEGER,DIMENSION(NLOOPLINE),INTENT(IN)::zerp
REAL(KIND(1d0)),DIMENSION(NLOOPLINE,0:3),INTENT(IN)::PDEN
REAL(KIND(1d0)),DIMENSION(NLOOPLINE,NLOOPLINE),INTENT(IN)::PijMatrix
REAL(KIND(1d0)),DIMENSION(NLOOPLINE),INTENT(IN)::M2L
INTEGER::idim
INTEGER,DIMENSION(NLOOPLINE)::indices
INTEGER,DIMENSION(0:NLOOPLINE)::paveindices
COMPLEX(KIND(1d0)),DIMENSION(0:NCOEFS-1,1:4),INTENT(OUT)::coefs
INTEGER,DIMENSION(xiarraymax,4)::sol
REAL(KIND(1d0)),DIMENSION(xiarraymax)::factor
REAL(KIND(1d0)),DIMENSION(NLOOPLINE-numzerp,0:3)::PCLL
INTEGER::i,j,k,init,r,nntot,nt,nindtot,nindtot0
LOGICAL::lzero
INTEGER,DIMENSION(0:NLOOPLINE)::nj
INTEGER,DIMENSION(0:NLOOPLINE,1:MAXRANK_IREGI)::jlist
REAL(KIND(1d0))::res,factemp
COMPLEX(KIND(1d0)),DIMENSION(1:4)::scalar
!REAL(KIND(1d0)),DIMENSION(xiarraymax)::coco
REAL(KIND(1d0)),DIMENSION(xiarraymax3)::coco
INTEGER,DIMENSION(MAXRANK_IREGI)::lor
coefs(0:NCOEFS-1,1:4)=DCMPLX(0d0)
j=1
nindtot0=0
DO i=1,NLOOPLINE
IF(zerp(i).NE.0)THEN
PCLL(j,0:3)=PDEN(i,0:3)
j=j+1
ENDIF
nindtot0=nindtot0+indices_init(i)
ENDDO
nt=NLOOPLINE-numzerp
DO i=1,ntot
r=sy(i,-1)
nntot=ntot_xiarray(r,4)
CALL all_integers(4,nntot,r,sol(1:nntot,1:4),factor(1:nntot))
lzero=.TRUE.
coco(1:nntot)=0d0
DO j=1,nntot
res=0d0
init=1
IF(sol(j,1).GE.1)THEN
lor(init:init+sol(j,1)-1)=0
init=init+sol(j,1)
ENDIF
IF(sol(j,2).GE.1)THEN
lor(init:init+sol(j,2)-1)=1
init=init+sol(j,2)
ENDIF
IF(sol(j,3).GE.1)THEN
lor(init:init+sol(j,3)-1)=2
init=init+sol(j,3)
ENDIF
IF(sol(j,4).GE.1)THEN
lor(init:init+sol(j,4)-1)=3
init=init+sol(j,4)
ENDIF
nj(0:nt)=0
jlist(0:nt,1:MAXRANK_IREGI)=0
CALL recursive_symmetry(nt,1,r,PCLL(1:nt,0:3),sy(i,-1:nt),lor(1:r),&
nj(0:nt),jlist(0:nt,1:MAXRANK_IREGI),res)
lzero=lzero.AND.(ABS(res).LT.EPS)
IF(.NOT.ML5_CONVENTION)THEN
coco(j)=res*factor(j)
ELSE
coco(j)=res
ENDIF
!coco(j)=res*factor(j)
ENDDO
IF(.NOT.lzero)THEN
indices(1:NLOOPLINE)=indices_init(1:NLOOPLINE) ! general form
idim=2*(r-sy(i,0))+idim_init
init=1
nindtot=nindtot0
DO j=1,NLOOPLINE
IF(zerp(j).NE.1)CYCLE
indices(j)=indices(j)+sy(i,init)
nindtot=nindtot+sy(i,init)
init=init+1
ENDDO
IF(IMODE.EQ.0)THEN
! IBP reduction
scalar(1:4)=scalar_integral_reduce2(NLOOPLINE,idim,indices,PijMatrix,M2L)
ELSE
IF(idim-2*nindtot+2*NLOOPLINE.GE.0.AND.indices(1).EQ.1)THEN
! PaVe reduction
! it can be improved as Gamma(ni+di)/Gamma(ni)*1/Gamma(ni+di), where 1/Gamma(ni+di) from factemp
CALL IBP2PAVE(NLOOPLINE,idim,indices,nindtot,factemp,paveindices)
scalar(1:4)=pavefun_reduce2(NLOOPLINE,paveindices,PijMatrix,M2L)*factemp
ELSE
scalar(1:4)=scalar_integral_reduce2(NLOOPLINE,idim,indices,PijMatrix,M2L)
ENDIF
ENDIF
IF(.NOT.STABLE_IREGI)RETURN
DO j=1,nntot
init=calc_pos(sol(j,1:4))
coefs(init,1:4)=coefs(init,1:4)+coco(j)*syfactor(i)*scalar(1:4)
ENDDO
ENDIF
ENDDO
RETURN
END SUBROUTINE general_symmetry2
SUBROUTINE general_symmetry(IMODE,NLOOPLINE,idim_init,indices_init,ntot,xiarraymax,xiarraymax2,xiarraymax3,&
sy,syfactor,numzerp,zerp,PDEN,M2L,NCOEFS,coefs)
! IMODE=0, IBP reduction
! IMODE=1, PaVe reduction
IMPLICIT NONE
INTEGER,INTENT(IN)::ntot,numzerp,NLOOPLINE,IMODE,NCOEFS,idim_init,xiarraymax2,xiarraymax,xiarraymax3
INTEGER,DIMENSION(NLOOPLINE),INTENT(IN)::indices_init
INTEGER,DIMENSION(xiarraymax2,-1:NLOOPLINE-numzerp),INTENT(IN)::sy
!INTEGER,DIMENSION(*,*),INTENT(IN)::sy
REAL(KIND(1d0)),DIMENSION(xiarraymax2),INTENT(IN)::syfactor
INTEGER,DIMENSION(NLOOPLINE),INTENT(IN)::zerp
REAL(KIND(1d0)),DIMENSION(NLOOPLINE,0:3),INTENT(IN)::PDEN
REAL(KIND(1d0)),DIMENSION(NLOOPLINE),INTENT(IN)::M2L
INTEGER::idim
INTEGER,DIMENSION(NLOOPLINE)::indices
INTEGER,DIMENSION(0:NLOOPLINE)::paveindices
COMPLEX(KIND(1d0)),DIMENSION(0:NCOEFS-1,1:4),INTENT(OUT)::coefs
INTEGER,DIMENSION(xiarraymax,4)::sol
REAL(KIND(1d0)),DIMENSION(xiarraymax)::factor
REAL(KIND(1d0)),DIMENSION(NLOOPLINE-numzerp,0:3)::PCLL
INTEGER::i,j,k,init,r,nntot,nt,nindtot,nindtot0
LOGICAL::lzero
INTEGER,DIMENSION(0:NLOOPLINE)::nj
INTEGER,DIMENSION(0:NLOOPLINE,1:MAXRANK_IREGI)::jlist
REAL(KIND(1d0))::res,factemp
COMPLEX(KIND(1d0)),DIMENSION(1:4)::scalar
!REAL(KIND(1d0)),DIMENSION(xiarraymax)::coco
REAL(KIND(1d0)),DIMENSION(xiarraymax3)::coco
INTEGER,DIMENSION(MAXRANK_IREGI)::lor
coefs(0:NCOEFS-1,1:4)=DCMPLX(0d0)
j=1
nindtot0=0
DO i=1,NLOOPLINE
IF(zerp(i).NE.0)THEN
PCLL(j,0:3)=PDEN(i,0:3)
j=j+1
ENDIF
nindtot0=nindtot0+indices_init(i)
ENDDO
nt=NLOOPLINE-numzerp
DO i=1,ntot
r=sy(i,-1)
! IF(r.EQ.0)THEN
! init=0
! ENDIF
nntot=ntot_xiarray(r,4)
CALL all_integers(4,nntot,r,sol(1:nntot,1:4),factor(1:nntot))
lzero=.TRUE.
coco(1:nntot)=0d0
DO j=1,nntot
res=0d0
init=1
IF(sol(j,1).GE.1)THEN
lor(init:init+sol(j,1)-1)=0
init=init+sol(j,1)
ENDIF
IF(sol(j,2).GE.1)THEN
lor(init:init+sol(j,2)-1)=1
init=init+sol(j,2)
ENDIF
IF(sol(j,3).GE.1)THEN
lor(init:init+sol(j,3)-1)=2
init=init+sol(j,3)
ENDIF
IF(sol(j,4).GE.1)THEN
lor(init:init+sol(j,4)-1)=3
init=init+sol(j,4)
ENDIF
nj(0:nt)=0
jlist(0:nt,1:MAXRANK_IREGI)=0
CALL recursive_symmetry(nt,1,r,PCLL(1:nt,0:3),sy(i,-1:nt),lor(1:r),&
nj(0:nt),jlist(0:nt,1:MAXRANK_IREGI),res)
lzero=lzero.AND.(ABS(res).LT.EPS)
IF(.NOT.ML5_CONVENTION)THEN
coco(j)=res*factor(j)
ELSE
coco(j)=res
ENDIF
!coco(j)=res*factor(j)
ENDDO
IF(.NOT.lzero)THEN
indices(1:NLOOPLINE)=indices_init(1:NLOOPLINE) ! general form
idim=2*(r-sy(i,0))+idim_init
init=1
nindtot=nindtot0
DO j=1,NLOOPLINE
IF(zerp(j).NE.1)CYCLE
indices(j)=indices(j)+sy(i,init)
nindtot=nindtot+sy(i,init)
init=init+1
ENDDO
IF(IMODE.EQ.0)THEN
! IBP reduction
scalar(1:4)=scalar_integral_reduce(NLOOPLINE,idim,indices,PDEN,M2L)
ELSE
! PaVe reduction
! it can be improved as Gamma(ni+di)/Gamma(ni)*1/Gamma(ni+di), where 1/Gamma(ni+di) from factemp
IF(idim-2*nindtot+2*NLOOPLINE.GE.0.AND.indices(1).EQ.1)THEN
CALL IBP2PAVE(NLOOPLINE,idim,indices,nindtot,factemp,paveindices)
scalar(1:4)=pavefun_reduce(NLOOPLINE,paveindices,PDEN,M2L)*factemp
ELSE
scalar(1:4)=scalar_integral_reduce(NLOOPLINE,idim,indices,PDEN,M2L)
ENDIF
ENDIF
IF(.NOT.STABLE_IREGI)RETURN
DO j=1,nntot
init=calc_pos(sol(j,1:4))
coefs(init,1:4)=coefs(init,1:4)+coco(j)*syfactor(i)*scalar(1:4)
ENDDO
ENDIF
ENDDO
RETURN
END SUBROUTINE general_symmetry
END MODULE gti_reduce
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